3.7.8 - Net present value and investment decisions

Time value of money and present values

A pound available now can be used or invested now, so it is not normally valued in the same way as a pound available several years later.

The time value of money reflects the opportunity to earn a return or make use of funds while waiting for a future receipt. Discounting converts a future cash flow into its equivalent value at the appraisal date, using a stated discount rate and timing convention. It is different from subtracting production costs or calculating accounting depreciation.

Use the supplied discount factors in the calculations. At a positive discount rate, a factor for a later receipt is normally lower because the wait is longer. A year-0 cash flow already occurs at the appraisal date, so its factor is 1. A negative future cash flow is discounted too and remains negative: timing does not convert an outflow into a benefit.

For a 10% annual discount rate, supplied factors are 0.909 for the end of year 1, 0.826 for year 2 and 0.751 for year 3. A £10,000 receipt has a different present value depending on its date. Use the factor for when the money is received, not a project's average factor.

Worked example 1 - identical receipts at different dates

Worked example 2 - discounting a future outflow

A £16,000 maintenance payment occurs at the end of year 2. Its supplied factor is 0.857.

It remains a cost in the appraisal; the lower present-value amount reflects timing, not an extra income receipt.

A discount rate represents a required return or opportunity-cost benchmark in the appraisal. It may reflect financing conditions and a risk allowance, depending on the stated basis. A higher rate reduces the present value of later positive inflows more strongly. The chosen rate does not make uncertain cash flows certain, and risk should not be hidden by an unexplained rate choice.

The factors are often rounded, so the final NPV can differ slightly from one calculated using unrounded factors. Use the supplied values, keep reasonable precision during working and round the final answer as requested. All cash-flow units must match: multiply a cash flow in £000 by its factor and keep the result in £000, or convert every value consistently to pounds.

Calculating net present value

Net present value, or NPV, is the total present value of a project's net cash flows, including its initial investment outflow.

An investment costs £50,000 at year 0 and generates net operating inflows of £20,000, £25,000 and £25,000 at the end of years 1, 2 and 3. A separate £5,000 residual receipt arrives at the end of year 3. There are no other flows.

Future present values total $£18{,}180+£20{,}650+£22{,}530=£61{,}360$. NPV is $£61{,}360-£50{,}000=£11{,}360$. Adding the signed column gives the same result. Omitting the residual would understate NPV by $£5{,}000\times0.751=£3{,}755$; adding it twice would overstate NPV by that amount.

Worked example 1 - adding the residual once

Worked example 2 - a project with a later cost

A project costs £72,000 initially. It provides net operating receipts of £42,000 at each of two year ends, with an additional £6,000 repair outflow in year 2. Factors are 0.95 and 0.90 respectively.

The small surplus could disappear after a modest adverse forecast change. Omitting the repair payment would exaggerate it by £5,400.

A positive NPV means forecast discounted net inflows exceed the initial cost at the chosen rate. A zero NPV means the forecast just meets that discount-rate benchmark. A negative NPV means it falls short. The £11,360 is a present-value surplus, not annual accounting profit, an immediate cash receipt or a guaranteed future bank balance.